[Python] Matplotlib log(log(x)) scale

I need a plot which doesn't fit the usual 'log-log' definition, but has a linear x scale and a double logarithmic y scale. I tried to create this in matplotlib with

import numpy as np
from matplotlib import pyplot as plt

# constants that result from other part of program
b = 9.144
c = -3.579

# values for plot
XL = np.linspace(273.15,373.15,101)
YL = 10 ** 10 ** (b + c * np.log10(XL)) - 0.7

# functions for scale transformation
def fw(x):
return np.log10(np.log10(x))

def bw(x):
return 10 ** 10 ** x

plt.plot(XL - 273.15, YL)
plt.yscale('function', functions=(fw, bw))
plt.show()


Please find this image for reference. However this program has two problems:

1. The y axis ticks start at 100 for a reason that I do not understand, leaving the largest part of the graph without any ticks.
2. I get the following warnings from NumPy regarding the log10 calls from fw(x):

RuntimeWarning: divide by zero encountered in log10
return np.log10(np.log10(x))
RuntimeWarning: invalid value encountered in log10
return np.log10(np.log10(x))


I get that probably the first warning leads to the second, but I do not see why there would be a division by zero. Any assistance to enlightenment on both problems would be greatly appreciated.

Continue reading...